Very interresting! I am not sure this demonstrated the aluminum repelling however. The coil was energized and what occurs is a magnetic field is created. The coil is held by stings and the magnetic field force is trying to equalize itself, so pushes off the secure aluminum plate lifting the coil in a effort to equalize the field that is restricted by the strings. I see it as the strings limiting the field from finding a neutral position so it sets up this bounding affect. I do not see the aluminum as a repelling force, I see it as a solidly mounted object, and the attaching strings as impeding the field from finding a position where it equalizes. I think if you did the same demonstration you could give the strings enough free length, so the magnetic field could have enough room to rise the coil and finds a equalizing position where the coil would remain steady. I could be wrong, but its a cool demonstation. Don't try this near the swimming pool or the lawnmower gas can.
The coil when it heats is a concept used in certain types of furnaces for creating high alloy metals, called induction furnaces I think. The outer core of the furnace is a coil that is energized and the field created by in causes extreme heat in the middle of the coil, melting the metal. It uses the magnetic field surrounding the coil, that is clashing in the center of the coil. Also this is the concept of the ignition coil in your car, energizing a coil with 12 volts, that builds up a magnetic field. mounted in the middle of the primary coil, is another coil called the secondary coil. When current to the primary is stopped (either by points or a pick up in the distributer) the magnetic field collapses, casuing a high voltage to be produced in the secondary that fires your spark plug.
Good Stuff Butcher--great subject.